欧拉分数与复阶参数斯特林、伯努利和欧拉函数及其对多对数函数的影响

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2023-01-01 DOI:10.2298/aadm220506002b

P. Butzer, T. He, C. Markett

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引用次数: 1

摘要

本文首先研究了复阶参数欧拉分数的一些推广，并研究了它们与类似的推广欧拉函数和斯特林函数的相互关系。我们将新方法应用于非整阶的多对数，其中只有少数值以封闭形式已知。特别地，我们提出了一个结构解的对应物的旧猜想孟格里和欧拉在多对数情况下黎曼?s函数和狄利克雷函数和函数。

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Eulerian fractions and Stirling, Bernoulli and Euler functions with complex order parameters and their impact on the polylogarithm function

We first study some generalizations of Eulerian fractions with complex order parameter and investigate their interrelationship with likewise generalized Eulerian functions as well as Stirling functions. We apply the new approach to polylogarithms of non-integral order, for which only a few values are known in closed form. In particular, we present a structural solution of the counterpart of an old conjecture of Mengoli and Euler in the polylogarithm case with the aid of Riemann?s zeta function and the Dirichlet eta and beta functions.

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来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).